Lucy there is no need to have a 'confrontation' with your daughter.
If you feel the need to be open about your conversations with the mutual friend , then the conversation should go like this:
1.DD, is it ok if I discuss something with you?
2. I feel very uncomfortable that you aren't happy about me chatting online to X. It makes me feel almost as though you are bullying me. (You are explaining the impact DD is having on you.
3. Wait for DD's response.
4. She'll either say you're imagining things, in which case the problem has gone away, or re-iterate that she doesn't want you to communicate with the mutual friend.
5.If the latter, ask her (gently) to explain why.
Concentrate on how she makes you feel, rather than criticising her.
I agree with others there is possibly more to this than meets the eye and it might be helpful to you both if things open up.
Good luck.